Modeling and Simulating Random Vectors with Given Marginals and Covariance Structure

Abstract

This research concerns the NORTA (NORmal To Anything) methodfor constructing a multivariate random vector having prespecified marginal distributions and prespecified correlations by applying anappropriate transformation of a standard normal random vector; and themain objective of this thesis is to develop an algorithm forestimating the normal correlations that are required to yield the desired correlations between the coordinates of the transformed random vector. A stochastic root finding method was implemented toapproximate the Normal correlations of interest with a prespecified level of accuracy. Examples are shown of the experimentationperformed with bivariate distributions having various marginals.Results are also shown for a bivariate distribution with two Uniform distributions as marginals, in which the functional relationshipbetween the Normal correlation and the prespecified correlation isknown exactly. The experimentation shows that this stochastic rootfinding algorithm is an excellent method for rapidly approximating the required Normal correlations to a reasonable degree of accuracy.